Open Access
Add to BibSonomy
Abstract
We present the design and optimization of the optical single side-band (SSB) Nyquist four-level pulse amplitude modulation (PAM-4) transmission using dual-drive Mach-Zehnder modulator (DDMZM)modulation and direct detection (DD), aiming at the C-band cost-effective, high-speed and long-distance transmission. At the transmitter, the laser line width should be small to avoid the phase noise to amplitude noise conversion and equalization-enhanced phase noise due to the large chromatic dispersion (CD). The optical SSB signal is generated after optimizing the optical modulation index (OMI) and hence the minimum phase condition which is required by the Kramers-Kronig (KK) receiver can also be satisfied. At the receiver, a simple AC-coupled photodiode (PD) is used and a virtual carrier is added for the KK operation to alleviate the signal-to-signal beating interference (SSBI).A Volterra filter (VF) is cascaded for remaining nonlinearities mitigation. When the fiber nonlinearity becomes significant, we elect to use an optical band-pass filter with offset filtering. It can suppress the simulated Brillouin scattering and the conjugated distortion by filtering out the imaging frequency components. With our design and optimization, we achieve single-channel, single polarization 102.4-Gb/s Nyquist PAM-4 over 800-km standard single-mode fiber (SSMF).
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber transmissions taking advantage of direct detection (DD)have drawn significant research efforts to increase the bit rate per channel to 100Gb/s and beyond [1,2]. In conventional intensity modulation and direct detection (IM/DD) systems, the resulted double side-band (DSB) signal suffers from the frequency selected power fading which is introduced by chromatic dispersion (CD). An efficient solution is to transmit the optical single side-band (SSB) signal by changing the transmitter [3]. Complex modulation with IQ modulator or dual-drive Mach-Zehnder modulator (DDMZM), and vestigial side-band filtering with an amplitude modulator and an optical filter, have been proposed to generate the SSB signal [4–6]. Among them, DDMZM provides a low-cost solution with simple one-bias control. In recent years, researchers have proposed and developed various advanced modulation formats to achieve high spectral efficiency (SE) that relaxes the bandwidth requirement on the optoelectronics in both the transmitter and receiver, such as discrete multi-tone (DMT) [7], carrier-less amplitude and phase (CAP) modulation [8], quadrature amplitude modulation (QAM) subcarrier modulation (SCM) [9], and pulse-amplitude modulation (PAM) [10]. In general, PAM-4 has a simple architecture and low power consumption, and has been selected for transmitting 400GbE over standard single mode fiber (SSMF) for client optics [11].
We have recently conducted a systematical investigation on DDMZM-based high speed optical SSB Nyquist PAM-4 transmissions [12–14]. The signal-to-signal beating interference (SSBI) due to the square-law detection of optical SSB is aggravated by the accumulated CD after fiber transmission, which is the main limitation factor of the transmission capacity and transmission distance. We have demonstrated an efficient hybrid equalizer combining feed forward equalizer (FFE) and third-order Volterra filter (VF) to compensate for SSBI, the inter-symbol interference (ISI), and nonlinearity in optical SSB transmissions [12].We have also demonstrated the effectiveness of SSBI mitigation by complex field signal reconstruction with Kramers-Kronig (KK) receiver in a PAM-4 transmission system [13].For a longer transmission distance, fiber nonlinearity also plays an important role. By inserting an optical filter, we have further tripled the transmission distance [14].
In this paper, we elaborate the design and optimization of optical SSB Nyquist PAM-4 transmissions using DDMZM modulation and DD. This paper is based on our previous work [12–14], but we continue discussing the requirement of the offset optical filtering and the joint optimization for the DD-KK receiver. At the transmitter, the optical SSB signal is generated by DDMZM after optimizing the optical modulation index (OMI), which can readily satisfy the minimum phase condition without resorting to a large positive bias. A narrow line width laser of 50-kHzis utilized to reduce the equalization-enhanced phase noise. At the receiver, a simple AC-coupled photodiode (PD) with KK operation is used to alleviate the SSBI by linearizing the DD receiver. After KK operation, the VF is cascaded to compensate for the ISI and the remaining nonlinearities. To combat the fiber nonlinearity, we find the offset optical filtering is beneficial and may be more practical than using digital signal processing (DSP).By an orchestra of these techniques, we experimentally demonstrate 102.4 Gb/s/λ optical SSB PAM-4 signal over 800-km SSMF at C-band. To the best of our knowledge, it is a record SSMF capacity-distance product of 81920 Gb/s × km for 100-Gb/s PAM-4 transmission using DDMZM and DD.
2. SSBI mitigation schemes
The mitigation of SSBI is critical in optical SSB systems and has been demonstrated through different approaches [15–17], such as receiver-based estimation and cancellation including single-stage linearization filter (SSLF) and VF. The SSLF has the simple structure without iteration, but it will introduce residual higher-order SSBI terms which limit the performance. The VF is dedicated to mitigate both the SSBI and fiber nonlinearity simultaneously, but its computation complexity can be unacceptable if it is used alone. Meanwhile, the emerging KK receiver has the advantage of reconstructing the optical phase digitally from the measurement of the optical signal’s intensity [18].Thus the square-law detection introduced SSBI can be mitigated by KK receiver.
The KK operation requires that the signal has to meet the minimum phase condition. Therefore, a large bias or optical carrier is normally added at the transmitter and a DC-coupled PD is required at the receiver [19, 20]. However, for high-speed operation, an AC-coupled PD is generally simpler and cheaper, and can avoid some side effects due to the DC drift. Different from [20], in our DDMZM based transmitter, the original DSB PAM-4 signal and its Hilbert transform with small amplitude are used as the in-phase and quadrature components and fed into the two ports of DDMZM which is biased at the quadrature point without resorting to a large bias. Then the generated optical SSB signal can easily satisfy the minimum phase condition [13]. In the receiver, we use an AC-coupled PD to detect the optical SSB signal, and the detected real valued DSB signal after analog-to-digital conversion (ADC) is expressed as,
where is the half-wave voltage and the second term is the SSBI.Since we use an AC-coupled PD in the DD-KK receiver, the detected current signal is not the minimum phase signal and the phase cannot be recovered directly. Fortunately, a virtual carrier can be inserted to the received signal to make the signal of minimum phase in the receiver DSP. We assume a positive constant, and define , such that and the trajectory of never encircles the origin. In this case, is a minimum phase signal [21]. Then the KK operation can be implemented. Figure 1 depicts the operation schematic of the simplified DD-KK receiver.
In Fig. 1, we simply add a virtual carrier, i.e. a positive value, at the DD-KK receiver to reconstruct the minimum phase signal. Then, the discrete-time signal of the received signal can be rewritten as,
where is a scaling factor and for the minimum phase condition. An up-sampling progress is needed before KK operation due to the high bandwidth resulting from the square root and logarithm operations. Subsequently, the KK relation between the phaseand the intensity ofis,where denotes the Hilbert transform. According to the recovered phase, the complex-valued optical SSB signal can be calculated as,Except for the SSBI, phase modulation to amplitude (PM-AM) noise, equalization-enhanced phase noise, devices bandwidth, fiber CD and nonlinearity are also limitations to the transmission performance. To sufficiently compensate for the distortions after KK operation, an enhanced hybrid equalizer which combines FFE and third-order VF are further used to compensate for the remaining distortions [12].3. System optimization and verification
3.1 Experimental setup
The experimental setup of the optical SSB Nyquist PAM-4 system is shown in Fig. 2. At the transmitter side, a pseudo random bit sequence (PRBS) with 218 bits is used for PAM-4 modulation and up-sampled to 2 samples per symbol for Nyquist pulse-shaping. The roll-off factor of the Nyquist filter is 0.1. The electrical dispersion compensation (EDC) is implemented in the frequency domain after recovering the complex-valued optical signal with the help of the Hilbert transform [22]. After that, the output sequence is down-sampled to 1.25 samples per symbol to achieve higher bit rate and the arbitrary waveform generator (AWG) is operating at 64 GS/s. Thus, the symbol rate is 51.2 GBaud, corresponding to the bit rate of 102.4Gb/s. Meanwhile, the scheme of 2 samples per symbol is also used when the AWG is operating at 56 GS/s, which corresponds to the bit rate of 56Gb/s. For DDMZM-based SSB modulation, the driving signals are two small signals and the DDMZM is biased at the quadrature point. For a DD system, the optimized carrier to signal power ratio (CSPR) is mainly limited by the nonlinearity of DDMZM. Therefore, it can be adjusted by changing the bias condition or the driving amplitude [22]. In our experiment, we control it via the OMI since the bias has been set at the quadrature point. The fiber link is comprised of straight-line multi-span 80-km SSMF with Raman fiber amplification (RFA). At the receiver side, the signal is first amplified by an Erbium-doped optical fiber amplifier (EDFA) to adjust the received optical power. Then, an optical band-pass filter (OBPF) is used to remove the out-of-band noise and conjugated distortion which is caused by fiber nonlinearity. The filtered signal is detected by one single AC-coupled PD followed by a digital processing oscilloscope (DPO) operating at 160 GS/s to perform signal detection and digitization. Then, the received discrete signal is processed in the offline DSP.
3.2 The optimization of the experimental system
3.2.1 The optimal OMI for SSB modulation
At first, we optimize the OMI to generate the optical SSB signal and meet the minimum phase condition. The OMI is defined as , where is the root-mean-square (RMS) of the electrical input to the DDMZM. As shown in Fig. 3(a), we use 0.13 and 0.15, respectively, for 56-Gb/s and 102.4-Gb/s signal transmission in back-to-back (B2B) with the optical signal-to-noise ratio (OSNR) around 30 dB. Figure 3(b) is the spectra of the generated optical SSB Nyquist PAM-4 signal at 56 Gb/s and 102.4 Gb/s with 0.02 nm resolution, where the side-band suppression ratios are higher than 10 dB. The signal bandwidth is halved with its brick-wall-like spectrum after Nqyuist pulse-shaping. The band widths are about 15.4 GHz for 56-Gb/s signal and 28.1 GHz for 102.4-Gb/s signal.
3.2.2 Effect of different laser line width
In general, laser phase noise is not critical to conventional IM/DD systems despite that there is PM-AM noise via chromatic dispersion. Our optical SSB transmission system resembles the coherent transmission system, since we can recover the phase information even by the direct detection and conduct electrical dispersion compensation. However, it has been discussed that there exists equalization-enhanced phase noise due to the electrical dispersion compensation [23], which puts a tighter constraint on the laser line width. Since we transmit the optical SSB signal beyond 100-Gb/s from 80-km to 800-km SSMF, we need to evaluate the effect from the laser line width. The strength of the laser phase noise can be characterized by the laser line width. We investigate the influence of the laser line width on 102.4-Gb/s Nyquist PAM-4 signal transmission over 80-km SSMF. Figure 4 is the BER curves with 1-MHz and 50-kHz laser line width at the optimal OMI. Clearly, the larger laser line width of 1 MHz results in a larger BER. By switching to a vendor specified 50-kHz laser, we can reduce the BER from 1.76 × 10−3 to 3.50 × 10−4. The insets (a) and (b) in Fig. 4 are the histograms of 50-kHz and 1-MHz laser line width at 5-dBm optical launch power. The noise for 1-MHz line width laser is more obvious than that with 50-kHz laser due to the spectrum expanding. Therefore, we use the laser with 50-kHz line width in our following experiment.
3.2.3 Fiber nonlinearity mitigation using offset optical filtering
For a longer transmission distance, the fiber nonlinearity comes into play. We may continue to use some DSP algorithms to combat it, but they can be computationally intensive with a limited performance improvement [24].In our experiment, we find it is handy to use offset optical filtering for alleviating multiple optical fiber nonlinear effects.
As shown in Fig. 5(a), after 80-km SSMF transmission, besides the optical carrier, the Stokes wave of stimulated Brillouin scattering (SBS) of the carrier appears at a frequency shift about 10 GHz. Meanwhile, the strong Kerr effect also causes significant spectrum broadening at one side of the carrier, the so-called conjugated distortion [24]. In this experiment, the OBPF at the receiver is an enabler of the long distance transmission by bringing three-fold benefits. It improves the sideband suppression ratio of the received SSB signal, rejects the SBS and conjugated distortion. In short, the OBPF removes the imaging spectral components on the upper side of optical carriers. The filter shape of the OBPF is also shown in Fig. 5(a). The OBPF has a 3-dB bandwidth of 52 GHz. The filter center wavelength is optimized by sweeping the filter and set at 1549.924 nm (wavelength index 5). Since the improper set of the center wavelength can reduce the optical CSPR (oCSPR) by filtering the carrier, there is a tradeoff between filtering the unwanted spectrum and keeping the optical carrier. Figure 5(b) shows the system performance and oCSPR by sweeping the filter wavelength. In our experiment, the oCSPR values are estimated by using the measured optical spectrum. After modulation, it is slightly difficult to estimate the power of the optical carrier in the presence of laser line width. Fortunately, the spectrum of the signal is flat since we use the Nyquist pulse-shaping. Hence we can measure the power spectrum density 0.1~0.15 nm away from the optical carrier and use extrapolation to estimate the total power due to the modulation. Thus we can separate the powers of the optical carrier and signal, and measure the oCSPR [22].The oCSPR is defined as , where is the optical carrier power and is the signal power.
Fig. 5 (a) Spectrum of optical SSB NPAM-4 with sweeping filter wavelength over 80-km SSMF; (b) The system performance and signal CSPR with sweeping filter wavelength over 80-km SSMF.
We also conduct a simulation of 112-Gb/s PAM-4 over 100-km SSMF to verify the necessity of the narrow OBPF using commercial software VPItransmissionMakerTM9.1. The OBPF is modeled as a Gaussian filter. The optical carrier is 1550 nm and the optical launch power is set at 10 dBm to generate strong fiber nonlinearity effects. The required order, bandwidth and center wavelength of the OBPF are tested. Figure 6(a) depicts the BER as a function of the order of Gaussian filter. The top axis represents the optimal filter bandwidth at different order of the Gaussian filter. The filter center wavelength is 1549.876 nm. Thus, the frequency interval between the filter center wavelength and optical carrier is approximately equal to the half-bandwidth of the SSB signal. When the filter order is higher than 3.5, the BER becomes saturated. Figure 6(b) is the optimal filter bandwidth versus the filter center wavelength for 3.5-order Gaussian filter. The center wavelength and bandwidth of the OBPF should be adjusted to avoid the signal distortion and reserve the carrier and side-band signal simultaneously.
Fig. 6 (a) Simulation of the order of Gaussian filter. (b) Optimal filter bandwidth with different filter center wavelength.
3.2.4 DC-filtering for signal sequence stabilization
Except for PM-AM noise, equalization-enhanced phase noise, and fiber nonlinearities, another limitation on system performance is related to the optical launch power. The received signal sequence shows some low-speed fluctuations at a high launch power, e.g. 5 or 7 dBm, due to the imperfections of the devices. It can be treated as the DC-drift and we add a DC-filtering step to stabilize the signal sequence despite we have used an AC-coupled PD. As shown in Fig. 7, before the DC filtering, there is a visible DC drift, which certainly affects the decision circuitry where a constant threshold is used. After the DC-filtering, the mean value becomes flat, which facilitates decision circuitry. This step can be skipped if we improve the parameters of the AC-coupled PD with a better suppression of the low frequency component around the DC.
3.3 The joint optimization for KK receiver
The KK receiver has the advantage of SSBI mitigation by optical field reconstruction. Figure 8(a) shows the spectra of the detected digital DSB signal and the reconstructed SSB signal, respectively. To conduct the KK operation, an up-sampling factor is needed to support the square root and logarithm operations. Figure 8(b) shows the BER versus the utilized sampling rate at the optimum launch power of 3dBm for the 56-Gb/s Nyquist PAM-4 signal transmission over 640-km and 800-km SSMF. The BERs significantly decrease when the sampling rate increases from 1 Sa/symbol to 2 Sa/symbol, and it converges for rate of 3 Sa/symbol. Meanwhile, the virtual carrier which is added in the receiver DSP needs to be large enough to satisfy the minimum phase condition. It is noted that the optimal results of sampling rate can also be used for other received optical powers, transmission distances and bitrates.
Fig. 8 (a) Detected DSB spectrum and the reconstructed SSB signal spectrum by the KK scheme; (b) BER at the optimum launch power versus resampling rate at 640 and 800km.
3.4 Comparison of SSBI mitigation schemes
After optimizing the setup, we compare the transmission performance with different SSBI mitigation schemes with 56-Gb/s PAM-4 signal. Fig. 9(a) depicts the transmission performance results with VF, SSLF and KK, respectively. The three SSBI mitigation methods are used to deal with the same received signal for a fair comparison. It can be found that only the KK followed by VF scheme is below the 7% hard-decision forward error correction (HD-FEC) threshold (3.8 × 10−3) after 640-km transmission, whereas the VF and SSLF methods are difficult to reach the 7% HD-FEC threshold. For 800-km SSMF transmission, the BER is below the 20% soft-decision forward error correction (SD-FEC) threshold (2.4 × 10−2). The inset (I) in Fig. 9(a) is the ratio of the Volterra kernels between the optical fiber nonlinearity and SSBI terms at 5-dBm launch power. The ratio of KK combines with VF is larger than that without KK, which implies that the VF mitigates both the SSBI and fiber nonlinearity simultaneously without KK. It is noted that the VF is dedicated to the mitigation of the fiber nonlinearity since the SSBI terms are mitigated after KK operation. The residual higher-order SSBI terms after SSLF limit the performance. Figure 9(b) is the transmission performance with FFE and VF after KK operation over 640-km SSMF. The results show that when the launch power is higher than 0 dBm, the VF is effective for fiber nonlinearity compensation compared with FFE.
Fig. 9 (a) BER with different SSBI mitigation schemes with 56-Gb/s PAM-4; (b) Transmission performance of KK receiver cascades FFE and VF with 56-Gb/s PAM-4. Insets: (I) ratio of the Volterra kernels, (II)-(IV) eye diagrams after VF, SSLF and KK at 3-dBm optical launch power after 640-km transmission.
3.5 Optical fiber transmission performance
At last, we test the system transmission performance of 102.4-Gb/s Nyquist PAM-4 signal with pre-EDC and KK receiver cascaded with VF. Figure 10(a) is the transmission performance with and without KK operation over 720-km SSMF at different optical launch power. After KK operation, the BER decreases from 2.73 × 10−2 to 1.54 × 10−2, which is below the 20% SD-FEC threshold. For KK, the corresponding factor improvement is 1.01 dB larger than that without KK, where.Fig. 10(b) shows the BER performance at different fiber lengths at the optimized optical launch power of 5 dBm. The BER of KK receiver is below 7% HD-FEC threshold over 400-km SSMF with a net rate of 95.7 Gb/s, and below 20% SD-FEC threshold over 800-km SSMF with a net rate of 85.3 Gb/s. The corresponding factor improvement is 0.86 dB with KK scheme over 800-km SSMF. Insets (III) and (IV) are the histograms with and without KK at 400-km SSMF, respectively. As we have discussed, the SSBI can be mitigated by KK operation which leads to the lower noise floor.
Fig. 10 (a) Transmission performance at 720 km. Insets (I) and (II) are the histograms with and without KK operation at 5 dBm. (b) BER versus transmission distance. Insets (III) and (IV) are the histograms with and without KK operation at 400-km SSMF.
4. Conclusion
We have experimentally demonstrated single-channel, single-polarization 102.4-Gb/s PAM-4 signal over 800-km SSMF at C-band using relatively lower-cost DDMZM and single AC-coupled PD. The design and optimization have been presented. Several methods have been proposed to overcome the impairments after long-distance fiber transmission. The narrow line width laser is used for less equalization-enhanced phase noise. The offset optical filtering method is used to filter the SBS and conjugated distortion. The cascaded KK and VF receiver has shown an excellent performance for SSBI mitigation and nonlinearities cancellation. We believe that optical SSB transmission using DDMZM and DD is potentially suitable for high-speed optical transmission over hundreds of kilometers SSMF.
Funding
National Natural Science Foundation of China (NSFC) (No.61405024, No. 61420106011, No.61471088); National High Technology Research and Development Program of China (863 Program) (2015AA015501).
References and links
1. Y. L. Gao, J. C. Cartledge, A. S. Kashi, S. S. H. Yam, and Y. Matsui, “Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation,” IEEE Photonics Technol. Lett. 29(1), 35–38 (2017). [CrossRef]
2. K. Zhong, X. Zhou, T. Gui, L. Tao, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “Experimental study of PAM-4, CAP-16, and DMT for 100 Gb/s Short Reach Optical Transmission Systems,” Opt. Express 23(2), 1176–1189 (2015). [CrossRef] [PubMed]
3. B. J. Lin, J. H. Li, H. Yang, Y. S. Wan, Y. Q. He, and Z. Y. Chen, “Comparison of DSB and SSB transmission for OFDM-PON,” in Proceedings of Optical Fiber Communication Conference (2012), paper NTu1J.7. [CrossRef]
4. L. Zhang, Q. Zhang, T. J. Zuo, E. B. Zhou, G. N. Liu, and X. G. Xu, “C-band Single Wavelength 100-Gb/s IM-DD Transmissionover 80-km SMF without CD compensation using SSB-DMT,” in Proceedings of Optical Fiber Communication Conference (2015), paper Th4A.2. [CrossRef]
5. L. Zhang, T. J. Zuo, Y. Mao, Q. Zhang, E. B. Zhou, G. N. Liu, and X. G. Xu, “Beyond 100-Gb/s Transmission Over 80-km SMFUsing Direct-Detection SSB-DMT at C-Band,” J. Lightwave Technol. 34(2), 723–729 (2016). [CrossRef]
6. H. Y. Chen, N. Kaneda, J. Lee, J. Chen, and Y. K. Chen, “Optical filter requirements in an EML-based single-sideband PAM4 intensity-modulation and direct-detection transmission system,” Opt. Express 25(6), 5852–5860 (2017). [CrossRef] [PubMed]
7. D. Pilori, C. Fludger, and R. Gaudino, “Comparing DMT Variants in Medium-Reach 100G Optically Amplified Systems,” J. Lightwave Technol. 34(14), 3389–3399 (2016). [CrossRef]
8. M. Xu, J. Y. Shi, J. W. Zhang, J. J. Yu, and G. K. Chang, “High-Capacity Tier-II Fronthaul Network with SSB-DD Multiband OQAM/QAM-CAP,” in Proceedings of European Conference and Exhibition on Optical Communication (2017), paper P2.SC8.58.
9. M. S. Erkılınç, Z. Li, S. Pachnicke, H. Griesser, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally Efficient WDM Nyquist Pulse-Shaped 16-QAM Subcarrier Modulation Transmission With Direct Detection,” J. Lightwave Technol. 33(15), 3147–3155 (2015). [CrossRef]
10. N. Eiselt, H. Griesser, J. L. Wei, A. Dochhan, M. Eiselt, J. P. Elbers, J. J. V. Olmos, and I. T. Monroy, “Real-Time Evaluation of 26-GBaud PAM-4 Intensity Modulation and Direct Detection Systems for Data-Center Interconnects,” in Proceedings of Optical Fiber Communication Conference (2016), paper Th1G.3. [CrossRef]
11. J. King, D. Leyba, and G. D. LeCheminant, “TDECQ (Transmitter Dispersion Eye Closure Quaternary) Replaces Historic Eye-mask and TDP Test for 400 Gb/s PAM4 Optical Transmitters,” in Proceedings of Optical Fiber Communication Conference (2017), paper W4D.1. [CrossRef]
12. M. Y. Zhu, H. Ying, J. Zhang, X. W. Yi, and K. Qiu, “Experimental demonstration of an efficient hybrid equalizer for short-reach optical SSB systems,” Opt. Commun. 409, 105–108 (2018). [CrossRef]
13. M. Y. Zhu, J. Zhang, H. Ying, X. Li, M. Luo, Y. X. Song, F. Li, X. T. Huang, X. W. Yi, and K. Qiu, “56-Gb/s Optical SSB PAM-4 Transmission over 800-km SSMF Using DDMZM Transmitter and Simplified Direct Detection Kramers-Kronig Receiver,”in Proceedings of Optical Fiber Communication Conference (2018), paper M2C.5.
14. M. Y. Zhu, X. W. Yi, J. Zhang, X. Li, M. Luo, F. Li, Z. H. Li, X. T. Huang, and K. Qiu, “102.4-Gb/s Optical SSB Nyquist-PAM-4 Transmission over 800-km SSMF at C-band Using Direct-Detection Kramers-KronigReceiver,” in Proceedings ofAsia Communications and Photonics Conference(2017), paper Su2B.3. [CrossRef]
15. F. Gao, S. Zhou, X. Li, S. Fu, L. Deng, M. Tang, D. Liu, and Q. Yang, “2 × 64 Gb/s PAM-4 transmission over 70 km SSMF using O-band 18G-class directly modulated lasers (DMLs),” Opt. Express 25(7), 7230–72372017). [CrossRef] [PubMed]
16. S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s Discrete-Multitone Transmission Over 80-km SSMF Using Single-Sideband Modulation with Novel Interference-Cancellation Scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697. [CrossRef]
17. Z. Li, M. S. Erkilinc, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24(25), 29176–29189 (2016). [CrossRef] [PubMed]
18. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3(11), 1220–1227 (2016). [CrossRef]
19. C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers-Kronig PAM transceiver and two-sided polarization-multiplexed Kramers Kronig transceiver,” J. Lightwave Technol. 36(2), 468–475 (2018).
20. C. Antonelli, M. Shtaif, and A. Mecozzi, “Kramers-Kronig PAM Transceiver,” in Proceedings of Optical Fiber Communication Conference (2017), paper Tu3I.5. [CrossRef]
21. A. Mecozzi, “A necessary and sufficient condition for minimum phase and implications for phase retrieval,” https://arxiv.org/abs/1606.04861.
22. Q. Zhang, N. Stojanovic, C. Xie, C. Prodaniuc, and P. Laskowski, “Transmission of single lane 128 Gbit/s PAM-4 signals over an 80 km SSMF link, enabled by DDMZM aided dispersion pre-compensation,” Opt. Express 24(21), 24580–24591 (2016). [CrossRef] [PubMed]
23. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]
24. Y. X. Zhu, K. H. Zou, and F. Zhang, “C-Band 112 Gb/s Nyquist Single Sideband Direct Detection Transmission Over 960 km SSMF,” IEEE Photonics Technol. Lett. 29(8), 651–654 (2017). [CrossRef]
